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Energy or speed needed to escape from the surface, a height or an orbit

This type of question, asked 3 times: 11 Apr 2023, 6 Apr 2024, 4 Apr 2025. All 4 questions below, oldest first.

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  1. Question 1

    11 Apr 2023

    101
    A spaceship is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if g=10 m/s2g = 10\text{ }m/s^{2} and radius of earth =6400 km= 6400\text{ }km )

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  2. Question 2

    6 Apr 2024

    4
    To project a body of mass mm from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE,g=R_{E},g = acceleration due to gravity on the surface of earth) :

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  3. Question 3

    4 Apr 2025

    14
    Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R . Assertion A : The kinetic energy needed to project a body of mass mm from earth surface to infinity is 12mgR\frac{1}{2}mgR, where R is the radius of earth. Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface. In the light of the above statements, choose the correct answer from the option given below

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  4. Question 4

    4 Apr 2025

    84
    An object is kept at rest at a distance of 3R3R above the earth's surface where RR is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume M=M = mass of earth, G=G = Universal gravitational constant)

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